Abstract

A simple dielectric hollow-tube has been experimentally demonstrated at terahertz range for bio-molecular layer sensing based on the anti-resonant reflecting wave-guidance mechanism. We experimentally study the dependence of thin-film detection sensitivity on the optical geometrical parameters of tubes, different thicknesses and tube wall refractive indices, and on different resonant frequencies. A polypropylene hollow-tube with optimized sensitivity of 0.003mm/μm is used to sense a subwavelength-thick (λ/225) carboxypolymethylene molecular overlayer on the tube’s inner surface, and the minimum detectable quantity of molecules could be down to 1.22picomole/mm2. A double-layered Fabry-Pérot model is proposed for calculating the overlayer thicknesses, which agrees well with the experimental results.

1. Introduction

Minute material detection is crucial for molecular recognition in many biological and chemical processes, especially in monitoring dynamic variation of the adsorbed molecular overlayer in the fluid channel. A highly sensitive and label-free sensing method would be useful for many applications, such as lab-on-a-chip, pollution detection equipment for environmental monitoring and industry, and medical diagnosis. Recently, remarkable developments have contributed to terahertz (THz) sensing technology based on the unique electromagnetic features of substances in THz range, making the label-free identification or detection of small quantities of analytes possible. Among various THz sensing modalities, sensing devices with engineering-resonant structures significantly increase the detection sensitivity and enable the detection of subwavelength-thick overlayers loaded in the vicinity of the resonant structure surfaces, or sensing small variations in a sample’s condition based on the strongly localized surface field. This sensing strategy has been extensively applied in metal hole arrays [1

]. Hence, a fiber-based resonant sensor is required to simultaneously confine light and analytes in the fiber’s hollow core or in the holes of the cladding region for fluid sensing. The fiber-based resonant sensor not only has an increased interacting length between light and analytes for highly sensitive detection, but its flexible structure is also advantageous in remote sensing. Several waveguide-based resonant sensors have been demonstrated in the THz range, including the THz parallel-plate waveguide sensor [8

] for detection of the deposited monolayer on the hollow-core surface of fibers. The calculated minimum detectable thickness is less than 1nm, which is comparable to the sensitivity of optical surface plasmon sensors [14

]. Accordingly, a resonant sensor, operating in the THz region, is necessary to extend the probing depth of the surface wave to a longer distance for macromolecular layer detection.

In this presentation, we experimentally demonstrate a THz-fiber-based resonant sensor employing a simple dielectric hollow-tube based on an anti-resonant reflecting hollow waveguidance (ARRHW) mechanism for sensing the subwavelength-thick molecular overlayer adhered to the inner-core surface of tubes. Due to the strongly localized THz evanescent wave at resonant frequency, which is much sensitive in the optical-path length of the tube-wall [13

], a tiny thickness variation of the molecular layer deposited near the tube wall will result in an obvious frequency shift of resonant dip in the transmission spectrum. We investigate the effects of the tube’s optical geometrical parameters, such as the different thicknesses or refractive indices of the tube-walls, and different resonant wavelengths on the thin-film detection sensitivity of the THz-ARRHW-resonant sensor by utilizing polyethylene (PE) films with different thicknesses attached to the tube’s surface. A polypropylene (PP) hollow-tube with optimized sensitivity of 0.003mm/μm is chosen to detect carboxypolymethylene molecular overlayers, which mimic biomolecular overlayers on the tube’s inner-surface. The variation of the minimum thickness of the biomolecular layers is calculated to be about 2.9μm (approaching 225 times less than the probing THz wavelength), corresponding to the detection limit of carboxypolymethylene molecules on the order of 1.22 picomole/mm2. A double-layered Fabry-Pérot model is proposed for theoretically calculating the thicknesses of the sample overlayers, and agrees well with the experimental results. The THz-ARRHW has potential for applications such as microfluidic channels and large bacteria detection.

2. Principle of thin film detection based on a THz-ARRHW

A THz-ARRHW is a hollow tube composited with a ring-shaped dielectric cladding and an air-core, and has been demonstrated for broadband and low-loss THz wave transmission [10

]. THz waves are reflected (antiresonanted) between the reflective ring-cladding which inherently serves as a Fabry-Pérot resonator, and then form the transmission peaks in a transmission spectrum. The resonant modes of the ring-shaped Fabry-Pérot resonator will leak in/outside the ring-cladding and form dips in a transmission spectrum [11

], and thus one can sense the tiny variation, index or thickness, of an adsorbed molecular film near the ring cladding. We propose a double-layered Fabry-Pérot model to simulate the sensing scheme based on the THz-ARRHW with a composite cladding consisting of a sample layer adhered to the waveguide cladding. The schematic cross-section diagram of the THz-ARRHW with a double-layered cladding for thin film sensing is illustrated in Fig. 1(a)

Fig. 1 (a) Cross-section of a THz-ARRHW with a double-layered cladding. n0, n1, n2 respectively denote refractive indices of air space, waveguide cladding, and sample layer, where n0 equals 1.0. R0, d1 and d2 are the hollow inner-core radius and different layer thicknesses. (b) The one-dimensional sketch illustrates the optical path of a THz wave propagated in the double-layered cladding, where θ0, θ1, θ2, are the refractive angles. Fabry-Pérot resonance occurs when θ0 approaches zero.

. A THz wave, propagated in a THz-ARRHW, will partially reflect and transmit at the interfaces of the double-layered cladding, and its one-dimensional optical path is shown in Fig. 1(b). As Fabry-Pérot resonance occurs, the electromagnetic wave phase of THz waves resonating in the reflective double-layered cladding should satisfy the condition, (d1n12−n02+d2n22−n02⋅ωm/C=mπ, where ωm is the resonant angular frequency, C is the speed of light in air, m is the resonant mode number which belongs to the integer, and d1,2, n1,2 are respectively the thickness and refractive index for a given layer in the cladding. Therefore, the resonant wavelengths for a THz-ARRHW can be derived as described in Eq. (1).

λm=2(d1n12−n02+d2n22−n02)m

(1)

We first apply the double-layered Fabry-Pérot model to study the resonant dip shift of the THz-ARRHW. Different PE films with standard thicknesses of 30, 60, 90μm, and a polymethylmethacrylate (PMMA) hollow tube were used, respectively, as the sample layer and waveguide cladding in the double-layered cladding geometry. Statistic measurement of PE film thickness through a microscope showed the percentage of thickness variation to be very small. The transmitted spectrum of a THz-ARRHW without the attached PE films can be reliably measured by THz time-domain spectroscopy (THz-TDS) [11

] and the wavelengths of resonant modes, i.e. dips in spectrum, could be accurately predicted by the theory of a Fabry-Pérot resonator. Figures 2(a)

Fig. 2 (a) A time-domain waveform for free-space THz pulses in the THz-TDS for the sensing works, where the waveform information for water vapor absorption is enlarged 10 times for observation. (b) A time-domain waveform of output THz pulses from a 30cm-long PMMA tube with a 4mm-inner core radius and a 1mm-thick tube-wall. (c) Different time-domain waveforms for standard PE films covering a PMMA tube with a 4mm-inner core radius and a 1mm-thick tube-wall.

and 2(b) show the time-domain waveforms of the THz pulses respectively in free space and output from a 30cm-long PMMA hollow tube. The scans were performed with a 133fs temporal resolution and typically 273ps-long to achieve a spectral resolution of 4GHz. The long-lasting oscillation of the temporal waveform has reserved the spectrum information of water vapor absorption and the broadened THz pulse. The PE films with different thicknesses were fully covered on the outer surface of the PMMA hollow tube with an inner radius of 4mm, and the resonant dips in transmission spectrum would be expected to shift based on the film thickness due to the change of the Fabry-Pérot resonance condition. Figure 2(c) shows the time-domain waveforms of the THz pulses transmitted through PMMA hollow tubes attached to PE films of different thicknesses, revealing that the waveform variations can be easily resolved based on the 133fs-temporal-resolution in THz-TDS measurement. Thicker PE film results in a more apparent waveform shift on the PMMA tube because of the increased optical-path-difference added on the bare tube.

Fig. 3 (a) The THz transmitted spectrum of a PMMA tube with a 4mm-inner-core radius covered by standard PE films on the overall outer surface. The resonant wavelengths of the bare PMMA tube for λ2, λ3 and λ4 are 1.280mm, 0.850mm and 0.640mm, respectively. The dotted lines denote the calculated resonant wavelengths for the standard PE films covered on the PMMA tube with a tube-wall thickness of 1.04mm, which is well consistent with the measured transmission dips. (b) The relation between the effective sample thickness and the wavelength shifts of different resonant modes. The standard PE films are used as the sample layers and the resonant modes are discussed at λ2, λ3 and λ4 for a PMMA tube with an inner core radius of 4mm and tube-wall thickness of 1.05mm.

illustrates the transmitted power spectra of a THz pulse along a 30cm-long PMMA hollow tube with standard PE films of different thicknesses. The transmission dips are shifted to long wavelength ranges for the increased thicknesses of the attached PE films. According to the measured resonant dips shown in Fig. 3(a) and the Fabry-Pérot resonance condition in Eq. (1), the measured thickness of the PMMA tube-wall can thus be calculated at 1.04mm, where the used refractive indices of PE and PMMA in Eq. (1) are 1.5 and 1.6, respectively [16

]. The wavelengths denoted by dotted lines in Fig. 3(a) are obtained from the recursive iteration of a PMMA tube-wall thickness at approximately 1.04mm into Eq. (1) to approach the measured transmission dips. The actual physical thickness of the tube-wall is statistically measured by a standard caliper. We cut a 30cm-long PMMA tube into 15 pieces with an average tube wall thickness of 1.05mm. The thickness value of 1.04mm calculated from the THz-ARRHW’s spectrum is reasonably close to the actual physical thickness of 1.05mm when considering the system uncertainty of THz-TDS in spectrum transformation from time-domain waveforms, which is around 4GHz at different resonant frequencies. The dip position in Fig. 3(a) is quite precise with an accuracy of nearly 4GHz during statistical THz-TDS measurements while the dip level is un-repeatable possibly due to the THz power fluctuation, but it does not affect the sensing results of the resonant-dip-shift. Therefore, the double-layered Fabry-Pérot model adopted to analyze the THz-ARRHW for subwavelength-thick films sensing is found to be successful. It should be noted that a specific sample layer loaded on the inside or outside surfaces of a given dielectric tube would have the same resonant dips and dip shifts in the transmission spectrum because of the same total optical path for THz waves in the composite cladding of the tube. Therefore, a THz-ARRHW sensor is suitable for sensing thickness variations of a thin analyte layer adhered to the inner surface of a given dielectric tube. Comparing the THz spectra of a tube with and without sample layers based on THz-TDS, the dip shifts can be observed in transmission spectrum and the thickness of a loaded sample layer could thus be estimated from Eq. (1).

3. Experimental results

A sensitive THz-ARRHW is essential when the thicknesses of the analyzed molecular overlayers are much smaller than the wavelengths of the THz waves. To choose a THz-ARRHW with the highest sensitivity for sensing thin biomolecular overlayer, we experimentally investigate the dependence of resonant dip shifts on resonant mode numbers and on optical geometric parameters of tubes, tube-wall thicknesses and indices. We used standard PE films with different thicknesses attached to the outer surfaces of various dielectric hollow-core tubes with tube-walls made of different materials and with different thicknesses. Because the interference of the THz waves in the composite cladding of a THz-ARRHW is dependent on the refractive index and the physical length of the propagation distances, we define the effective cladding and sample thicknesses asτcldorfim=d1,2n1,22−n02.

For the standard PE films attached to the outer surface of a PMMA tube with a 4mm-inner core radius and 1.05mm-thick tube-wall, the dip shifts at different resonant wavelengths λm are not the same, as shown in Fig. 3(a) and resulted from the different thicknesses of the PE films corresponding to different effective sample thicknesses. We plotted the dependence of resonant wavelength shifts, Δλm, on the effective sample thicknesses, τfim, as illustrated in Fig. 3(b). The slope of the linear fit at each resonant wavelength, shown in Fig. 3(b), is defined as the thin film detection sensitivity of the THz-ARRHW, and the sensitivity rises as the resonant mode number m decreases, equivalent to a longer resonant wavelength. For example, Fig. 3(b) shows the measured second resonant mode, λ2, of the 1.05mm-thick PMMA tube is located at a wavelength of 1.280mm with sensitivity of λ2 as 0.0013mm/μm, meaning that the addition of 1μm effective sample thickness τfim onto the waveguide cladding induces 0.0013mm wavelength shift Δλ2. The sensitivity values for resonant modes, λ3, λ4 are 0.0009mm/μm and 0.0006mm/μm, respectively, which are both lower than the sensitivity value for λ2. The measured vertical-axis deviation, illustrated in Fig. 3(b), is estimated from the frequency inaccuracy in the THz-TDS measurement, which is around 4GHz, and the thickness (horizontal-axis) variations of the standard PE films were statistically measured with a microscope. By differentiating Eq. (1) to obtain the dependence of slight variations for the mth resonant wavelength on slight variations of the effective sample thickness, we may define the theoretical sensitivity in thickness detection for a given THz-ARRHW as, Sλ=∂λm∂τfim=2m. From the above formula, the sensitivity Sλ is inversely proportional to the resonant mode number, m, for a given THz-ARRHW. Therefore, the low order resonant mode (i.e. at longer resonant wavelengths) provides the high sensitivity required for sensing subwavelength films as shown in Fig. 3(b).

When we increase the wall thickness of the PMMA tube to 1.99mm, the thin film detection sensitivity at each resonant wavelength, calculated from the linear fit slope, decreases compared with that of a PMMA tube with a 1.05mm-thick wall, illustrated in Fig. 4(a)

Fig. 4 (a) The relation of sensitivity and resonant modes for 1.05mm- and 1.99mm-thick PMMA tubes. (b) The relation of sensitivity and effective cladding thickness.

. The error bars in Fig. 4(a) are produced from the frequency uncertainty of THz-TDS measurement at spectrum ranges near each resonant wavelength, which are +/−23.5%-, +/−13.1%- and +/−6.8%-variations corresponding to wavelength ranges of 0.6~0.8mm, 0.8~1.0mm and 1.0~1.3mm, respectively. Figure 4(a) only indicates how the tube-wall thickness affects the thin film sensing capability without considering the effect of the tube refractive index. To consider the effects of both thickness and the tube-wall index on sensing capability, we used the overall optical path length of the double-layered cladding, including effective cladding thicknesses τcld and effective sample thickness τfim, and redefined the thin film detection sensitivity as Sλ=λmτcld+τfim. From the above formula, we can see a tube with a high sensitivity should have a small effective cladding thickness when the dip shifts are observed at a specific resonant wavelength. Therefore, the highly sensitive THz-ARRHW sensor has a small effective cladding thickness, equivalent to a small physical thickness or a small refractive tube-wall index, and the induced dip shift in the transmission spectrum due to the sample overlayer would be apparent at low resonant mode numbers. Usually, the contribution of a tube-wall index for the small effective cladding thickness is limited and is dominated by the physical thickness. In other words, the sensitivity of the ARRHW-based sensing scheme is dependent on the percentages of the evanescent power around the tube-walls at each THz resonant mode. For a low index or a small physical thickness of tube-wall, a resonant THz wave in the waveguide cladding will be loosely confined and result in more THz evanescent power leakage in/outside the tube-wall, which is thus much more sensitive in detecting the molecular overlayer near the waveguide cladding. On the other hand, for a certain tube-wall thickness, the longer resonant wavelengths (i.e. the lower-order resonant modes) would leak much more evanescent power and perform at higher sensitivity compared with the shorter resonant wavelengths.

Figure 4(b) shows the dependence of the measured sensitivities on THz-ARRHWs with different effective cladding thicknesses, in which the sensitivities are determined from the maximum slopes located in the wavelength range of 0.5~2.0mm. The focused THz beam diameter is kept around 4mm to minimize input coupling loss when the inner core diameters of the THz-ARRHWs (i.e. 6, 8 and 12mm in this research) are larger than the THz beam. Aside from the PMMA tubes, glass (n~2.6) and polypropylene (PP; n~1.5) tubes were also used in the experiment. As shown in Fig. 4(b), the THz-ARRHW’s measured thin film detection sensitivity can be up to approximately 0.0030mm/μm for the PP tube with a 12mm-inner core diameter and a 0.29mm-thick-tube wall, and the sensitivity trend for different effective cladding thicknesses is consistent with the above discussion. The deviations of the effective cladding thicknesses in Fig. 4(b) are determined only from the physical thicknesses of tube-walls without concern for their refractive indices, and the thickness variation along each tube is between 2~10%, dependent on the different materials and thicknesses.

We chose the PP tube with the highest measured sensitivity for the detection of micro-molecular overlayer adhered on the inner-core surface of the tube. The PP tube used in the micro-molecular layer sensing experiment has length of 15cm with a small cladding thickness of around 0.29mm, and a 12mm inner-core diameter. The micro-molecular layers were prepared from various aqueous concentrations of carboxypolymethylene powder (carbopol 940, Boai Nky Pharmaceuticals Ltd.) dissolved in water, including 1%-, 2%-, 3%- and 4%-weight concentrations. Carbopol 940 is one kind of macromolecular material with a molecular weight of 104000g/mole and including 1450 monomer units [17

]. We fabricated the micro-molecular layer through the gravity-driven flow of viscous carbopol liquids in the PP tube. The hollow core of a PP tube was first filled with the viscous fluid and then allowed to stand to make the liquid flow freely through the tube. Liquid film could then spread and be adsorbed on the inner-core surface of the tube and pulled by gravity until the water had evaporated leaving a dry-solid layer. Based on the resonant characteristics of the PP THz-ARRHW, the thickness variations of the adsorbed micro-layers from different concentrations of carbopol molecules could thus be detected. The inset of Fig. 5

Fig. 5 The relation between the concentrations and calculated thicknesses of carbopol-micro-molecular layers; (inset) different spectrum positions of the first resonant mode for a PP tube with a 0.29mm-thick tube-wall. The thickness deviation (vertical-axis error bars) comes from the 4GHz frequency inaccuracy of the THz-TDS system.

shows the first resonant mode λ1 of the 0.29mm-thick PP tube, located at 0.654mm, is shifted when different thicknesses of micro-molecular layers are adhered to the PP-cladding, resulting from different viscosities of carbopol solution [18

]. Adsorbed micro-molecular layers from 1%-, 2%-, 3%- and 4%- carbopol aqueous solutions resulted, respectively, in shifted dip wavelengths of 0.661mm, 0.669mm, 0.676mm and 0.700mm. The thicknesses of the carbopol molecular layer were obtained through Eq. (1) and are illustrated in Fig. 5, where the THz refractive index of the carbopol-layer is around 1.2 as measured from a bulk carbopol material using THz-TDS. The calculated thicknesses of the carbopol-micro-molecular layers for 1%-, 2%-, 3%- and 4%- concentrations are 5.3μm, 11.3um, 16.7μm and 34.3μm, respectively. Based on the 4GHz frequency resolution of THz-TDS (at 0.654mm wavelength), converting the wavelength resolution of 0.0057mm, and the 0.0030mm/μm-sensitivity of the PP tube, the calculated minimum detectable thickness-increment for the carbopol-layer approaches 2.9μm (~λ/225), which corresponds to the minimum detectable quantities of carbopol molecules in the micro-overlayers be as low as 126.88 ng/mm2 or 1.22 picomole/mm2. G. Klatt et al. presented an efficient THz-TDS through the asynchronous optical sampling (ASOPS) method, providing a minimum resolved spectrum width of around 1GHz [19

]. It could potentially be integrated with a THz-ARRHW sensor to decrease the detectable thickness of the overlayer approaching to sub-micrometer (~0.72μm). It should be noted that the bandwidths of the resonant dips shown in the inset of Fig. 5 are obviously broadened for the thick layers because of the decreased visibility in the THz-ARRHW interferometer. In theory, equal intensity of interfered waves results in high visibility [20

]; however, the decreased visibility in this case is resulted from the high absorption of the secondary-reflected THz waves in the thick sample layers.

4. Conclusion

In summary, we experimentally demonstrate a THz-fiber-based-resonant sensor using a simple dielectric hollow-tube based on the anti-resonant reflecting hollow waveguidance mechanism for sensing a subwavelength-thick molecular overlayer adhered to the inner-core surface of a tube. The effects of the tube optical geometric parameters and different resonant wavelengths on the thin-film detection sensitivity of the THz-ARRHW-resonant sensor are also investigated, indicating a small physical thickness or a small tube-wall refractive index and a longer resonant wavelength will induce an apparent dip shift in the transmission spectrum. The measured minimum detectable thickness variation of the micro-molecular layer is about 2.9μm (~λ/225), corresponding to the detection limit of carbopol molecules on the order of 1.22 picomole/mm2, which is demonstrated on a PP tube with a sensitivity of 0.0030mm/μm. A double-layered Fabry-Pérot model is proposed for theoretically calculating the thicknesses of the sample overlayers, which well agrees with the experimental results. The THz-ARRHW could potentially be applied in fluidic channels for real-time monitoring of molecular interactions, and to detect various bacteria with sizes of several microns.

Acknowledgment

This work was supported by the Advanced Optoelectronic Technology Center, National Cheng Kung University, under projects from the Ministry of Education and the National Science Council (NSC 98-2221-E-006-014-MY2) of Taiwan.

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